CN104299260B - Contact network three-dimensional reconstruction method based on SIFT and LBP point cloud registration - Google Patents
Contact network three-dimensional reconstruction method based on SIFT and LBP point cloud registration Download PDFInfo
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Abstract
The invention provides a contact network three-dimensional reconstruction method based on SIFT and LBP point cloud registration. The method comprises the first step of obtaining initial three-dimensional point cloud data of the environment where parts of a contact network to be reconstructed are located through motion-sensing peripheral Kinect for Windows, and conducting denoising, simplifying, partitioning clustering, fusing and other preprocessing operations on the initial three-dimensional point cloud data to obtain single-view-angle point cloud data of the parts of the contact network to be reconstructed, the second step of extracting key points through an SIFT algorithm, constructing description vectors of the key points by means of LBP features of uniform patterns and determining the corresponding relations between the key points in different point clouds according to the distances between the vectors, the third step of completing point cloud registration through a rough registration method and an ICP fine registration method and obtaining the complete three-dimensional point cloud data of the parts of the contact network to be reconstructed, and the fourth step of completing three-dimensional reconstruction through the Poisson surface reconstruction method and obtaining a three-dimensional model. According to the method, the key factor is point cloud registration which is the key step influencing the three-dimensional reconstruction speed; the description vectors of the key points are constructed by means of the LBP features of the uniform patterns, so that vector dimensions are reduced, the matching speed of the corresponding relations is increased, registration is accelerated, and the three-dimensional reconstruction speed is increased.
Description
Technical field
The present invention relates to electric railway suspension arrangement threedimensional model obtains field, it is considered to which three-dimensional reconstruction process point cloud is matched somebody with somebody
Quasi- method.
Background technology
, used as the body frame structure of railway electrification project, its threedimensional model is in staff training, fault detect, contact net for contact net
Application prospect in terms of parameter designing is extensive[1,2,3].At present, being adopted mostly with regard to elements of contacting net threedimensional model
The three-dimensional softwares such as 3DMax are simultaneously drawn with reference to each catenary's parameterses, and time-consuming, workload big needed for acquisition model and obtains mould
Type differs larger with realistic model.So new automatization's method for reconstructing is required, concrete thought is：Using optical scanner
The cloud data of each parts of contact net is obtained, and it is many by what is obtained without measurement under visual angle with certain point cloud registration algorithm
The conversion of piece point cloud is merged into one complete point cloud data of formation under the same coordinate system, and then Jing curve reestablishings obtain each with rendering
Part threedimensional model.
Three-dimensional reconstruction research currently with depth data is relatively broad, there is point cloud simplification, point cloud registering and application aspect,
But on the whole the applied research in terms of the three-dimensional reconstruction of parts of electrified railway contact network does not almost have.
Document " Cai's width. the three-dimensional reconstruction based on a cloud studies [D]. Harbin Institute of Technology's master thesis,
2010. " and " Wang Erzhu. based on a cloud three-dimensional reconstruction system research with realize [D]. Harbin Institute of Technology's master's degree opinion
Text, 2011. " describe a kind of new three-dimensional rebuilding method, and give the basic process and flow process of reconstruction, in addition, also carrying
A kind of method for simplifying of new magnanimity spatial point cloud data is gone out.The method is with magnanimity spatial point cloud data at random to be input into number
According to, non-uniform grid method and the curvature method of simplifying are combined and cloud data is simplified, each discrete point k nearest neighbor is searched for first simultaneously
Obtain its least square curved surface, calculating method resultant curvature, Jing global adaptations, it is ensured that the global coordination of method arrow, then carry out essence
Letter.K nearest neighbor search method therefor is Kd-Tree neighbor search methods, and it is parabola fitting that least square curved surface obtains method therefor
Method, simplifies algorithm and uses non-uniform grid method and curvature to simplify method.
Document " Chu is sent out. the design and realization [D] based on the three-dimensional registration system of body-sensing. Shanghai Communications University's master's degree
Paper, 2011. " to design and develop based on the three-dimensional registration system of body-sensing, the system is designed using multisystem structure, bottom base
The collection of three-dimensional information is carried out in Microsoft's Kinect for windows somatosensory devices, using OpenNI frameworks driving of increasing income, is pressed
Photograph is extracted like point assessment, Coordinate Conversion and point cloud alignment carry out point cloud registering, while considering the efficiency of system and the effect of registration
Coordination between fruit.Quick point feature histogram (Fast Point Feature Histograms, FPFH) algorithm is done in system
Improve, propose triangle normal feature histogram (Triangle Normal Feature Histograms, TNFH) algorithm, only
Using triangular facet normal angle feature, the process for making feature calculation is simplified, and and characteristic quantity low compared with FPFH algorithm complexes
Less, and the registering rate of FPFH is kept.
Document " Liu Qiulong, Hu Wusheng. carry out Hui Quan transformer stations three-dimensional reconstruction [J] using cloud data. ground ore deposit is surveyed and drawn,
2009,25(4):7-8. " proposes the scheme for carrying out three-dimensional reconstruction to transformer station with cloud data, sweeps first with laser
Retouch the cloud data that instrument gathers object difference angle to be reconstructed；Then the automatic Mosaic of adjacent angular cloud data is carried out, is formed
Complete point cloud；Point cloud characteristic curve is finally extracted, with reference to coplanar condition, the threedimensional model of object to be reconstructed is generated, transformer station is completed
Three-dimensional reconstruction and model visualization.
The content of the invention
In view of prior art is not enough above, it is an object of the invention to provide a kind of three-dimensional reconstruction of elements of contacting net
Method, the method is that the elements of contacting net cloud data to be reconstructed using three-dimensional point cloud treatment technology to getting carries out pre- place
Reason, registration, fusion and curve reestablishing, obtain threedimensional model.Its core is that three-dimensional reconstruction point cloud registration Algorithm has been made to improve,
After key point is extracted using SIFT algorithms, key point description vectors are built using the LBP features of uniform pattern, then carried out
Subsequent registration process and three-dimensional reconstruction, obtain threedimensional model.This improvement improves the speed of point cloud registering, and to registration effect shadow
Ring little, so as to accelerate three-dimensional reconstruction.
The purpose of the present invention is realized by following means：
A kind of elements of contacting net three-dimensional rebuilding method of the point cloud registering based on SIFT and LBP, by Kinect device
Elements of contacting net three dimensional point cloud to be reconstructed is obtained, comprising following means：
(1), elements of contacting net three dimensional point cloud is obtained and pretreatment
Oni format videos are obtained using Kinect for Windows equipment and with reference to the Niviewer.exe in OpenNI
Data, then convert video data to pcd form cloud data files, so as to obtain contact to be reconstructed with point cloud storehouse PCL
The initial three-dimensional data of net parts place environment；Initial three dimensional point cloud to getting carries out denoising, simplification, splits and gather
The pretreatment operations such as class, fusion, obtain elements of contacting net three dimensional point cloud to be reconstructed.
(2) it is, special with Scale invariant to three dimensional point cloud under each visual angle of elements of contacting net to be reconstructed acquired in (1)
Levy conversion (SIFT：Scale Invariant Feature Transform) algorithm, extracts SIFT key points；Then, using equal
Image local binary pattern (the LBP of even pattern：Local Binary Patterns) feature description is carried out to key point, obtain
Each key point feature description vector；Then, measure distance between vector as similarity determination between key point, and determined not with this
With the corresponding relation put under visual angle between cloud；Finally, a cloud rough registration and closest approach iteration (ICP are carried out：Iterative
Closest Point) essence registration, obtain elements of contacting net Complete three-dimensional cloud data to be reconstructed.
(3), curve reestablishing is carried out to (2) data using Poisson curved planar reformation, hole repair, stricture of vagina is carried out to obtained model
Reason addition etc., finally obtains the threedimensional model of elements of contacting net to be reconstructed, completes process of reconstruction.
In the inventive method, three dimensional point cloud acquisition methods separately carry out data acquisition and three-dimensional reconstruction, solve
The problem high to each hardware device configuration requirement, beneficial to being smoothed out for common three-dimensional reconstruction.
In the method for the present invention, LBP features in combination with the extraction of SIFT key points, are carried out key point by point cloud registration method
Extraction and feature description, greatly reduce the dimension of key point description vectors, accelerate the speed of point cloud registering, so as to accelerate three
Dimension is rebuild.
The concrete steps that above-mentioned (2) and (3) implement are included：
(1) SIFT key points are extracted
A, metric space feature point detection, i.e., detect Local Extremum, in this, as key in difference of Gaussian pyramid
Candidate target is put, metric space used and difference of Gaussian function are as follows,
Metric space：
Difference of Gaussian function：D (x, y, σ)=L (x, y, k σ)-L (x, y, σ)
G (x, y, σ) is gaussian kernel,I (x, y) is image intensity；σ yardsticks；K is normal
Amount；
B, key point are accurately positioned, yardstick determines and the rejecting of unstable candidate key point；By digital simulation curved surface
Extreme value determining exact position and the yardstick of key point, while rejecting the low characteristic point of contrast and unstable skirt response
Point, to improve the stability and noise immunity of matching；
The determination of C, key point principal direction；The gradient-norm of each pixel and direction are respectively in metric space：
θ (x, y)=tan-1((L(x,y+1)-L(x,y-1))/(L(x+1,y)-L(x-1,y)))
Gradient orientation histogram is created, selects histogrammic main peak value to be key point principal direction；
(2) the invariable rotary uniform pattern LBP feature descriptions of key point peripheral region
A, in SIFT key points piIn the k nearest neighbor region of (x, y, z, σ, α, beta, gamma), respectively with each point pjCentered on, ask
The invariable rotary uniform pattern LBP features being able to centered on itIt is designated as lbpj(j=1,2 ..., K)；
gi、gcIt is respectively the gray value of the gray value of sampled point and intermediary image vegetarian refreshments in neighborhood；P is sampling number；R is to adopt
Sample radius；
B, addition weighted value, ωj=exp (- (d2/(2σ0 2)))/(2πσ0 2)；
D is point pjWith key point piBetween distance；σ0For the constant selected；
C, characteristic vector build, Ti=[ω1·lbp1 ω2·lbp2 … ωK·lbpK]；
D, normalized eliminate illumination effect, i.e.,
(3) SIFT keys Point matching, determines corresponding relation；
Decision metric is the distance between vector, is expressed as follows：
TA, TBIt is respectively the LBP feature descriptions vector of key point A and B；ai、biBe respectively A and B LBP feature descriptions to
Each dimension element of amount；
Matching strategy is：Key point A in a cloud 1 is taken, two nearest with its feature description vector distance are found out in a cloud 2
Individual key point B and C, if minimum distance is less than certain threshold value t with secondary in-plant ratio, then it is assumed that closest with key point A
Key point B match with it, i.e.,
(4) point cloud registering
After 2 cloud corresponding relations determine, registration is carried out to a cloud, rough registration and essence two processes of registration can be divided into；Slightly
Registration adopts PCA PCA (Principal Components Analysis), and essence registration is using ICP essence registration methods；
A series of point cloud registerings of Jing obtain complete elements of contacting net three dimensional point cloud to be reconstructed；
(5) using Poisson curved planar reformation, curve reestablishing is carried out to obtained complete point cloud data, obtains contact net to be reconstructed
Parts threedimensional model；
The registration of three-dimensional reconstruction process point cloud is carried out according to this point cloud registration method, accelerates point cloud registering speed, from
And accelerate process of reconstruction, obtain elements of contacting net threedimensional model to be reconstructed.
Compared with prior art, it is using the beneficial effects of the method for the present invention：
1st, three-dimensional model acquiring method of the present invention is Computerized 3 D visual technology, with contact net to be reconstructed zero
The three dimensional point cloud of part is process object, final to obtain by processes such as point cloud pretreatment, point cloud registering, curve reestablishings
Threedimensional model, the method is relative to direct drawing three-dimensional model, high degree of automation, the difference between model and actual object feature
Few, model is more accurate.
2nd, the present invention is directed to this defect of point cloud registering process restriction reconstruction speed during three-dimensional reconstruction, with uniform mould
Point cloud registration method of the formula LBP feature in combination with SIFT algorithms carries out point cloud registering, point cloud registering speed is improved, so as to accelerate
Process of reconstruction.
As described above, the method pin that the present invention is adopted is slow for the three-dimensional reconstruction speed of elements of contacting net, automatization's journey
Low defect is spent, with the contact net three-dimensional rebuilding method based on point cloud registerings of the SIFT in combination with uniform pattern LBP, is realized
The purpose of the rapid automatized reconstruction of elements of contacting net.
Description of the drawings
Fig. 1 data preprocessing flow charts
Fig. 2 obtains oni video data surface charts.
Fig. 3 initial points cloud visualization figure.
Insulator portion cloud data visualization figure after Fig. 4 pretreatment, Fig. 4 (a) does not contain RGB, and Fig. 4 (b) contains RGB.
Fig. 5 insulator key point extraction effect figures, Fig. 5 (a) visual angles 1, Fig. 5 (b) visual angles 2.
Comparison diagram before and after Fig. 6 insulators registration.
Insulator completely puts cloud visualization figure after the completion of Fig. 7 is registering.
The processing speed relative analyses of Fig. 8 SIFT algorithms and inventive algorithm.
The three-view diagram of Fig. 9 insulator Three-dimension Reconstruction Models.
Figure 10 rod insulators material object and reconstruction model comparison diagram.
Figure 11 section insulators material object and reconstruction model comparison diagram.
Figure 12 disc insulators material object and reconstruction model comparison diagram.
Specific embodiment
Embodiments of the present invention are described in further detail below in conjunction with the accompanying drawings, and protection scope of the present invention is not limited to
Following embodiments.
Fig. 1 is data preprocessing flow chart.
A, cloud data are obtained
Oni format videos are obtained using Kinect for Windows equipment and with reference to the Niviewer.exe in OpenNI
Data, then convert video data to pcd form cloud data files, so as to obtain contact to be reconstructed with point cloud storehouse PCL
The initial three-dimensional data of net parts place environment, obtains interface as shown in Fig. 2 the visualization of initial point cloud is as shown in Figure 3.
B, elements of contacting net data preprocessing to be reconstructed
A, three dimensional point cloud denoising
Due to being affected by factors such as artificial disturbance, illumination, scanning device self-defects, three dimensional data collection equipment obtains true
Real object surface data can receive sound pollution, it is impossible to correct true reflection object locus, therefore need to carry out denoising to it.
Effectively denoising can keep the sharp features of point cloud model while denoising, prevent the excessively fairing of obtained model.It is general next
Say, gaussian filtering is higher for the preservation of data original appearance, and medium filtering is then more obvious for the elimination of data burr.
B, cloud data simplify
Initial point cloud data volume is big, there are redundant points, and the method that need to pass through to filter is removed, so as to reduce storage area, plus
Cloud processing speed as soon as possible.Simplified using stochastical sampling and uniform grid etc. typically for dispersion point cloud；For scan line and
Polygon point cloud is simplified using "flop-out" method；For grid point cloud is carried out using methods such as Minimum Area encirclements and distribution density
Simplify.
C, cloud data segmentation
When cloud data amount is huge, single treatment is more difficult, can by the way that complete point cloud data is divided into into some fritters,
Then the mode of the reply archetype shape such as fused matching reduces the point cloud quantity of each data processing, and then improves three-dimensional
The efficiency and accuracy of reconstruction.The curvature of segmentation selected areas should change less, where curvature is more smoothed, so can reduce
The deformation probability of model.
D, point cloud data fusion
Some independent point clouds on model are merged into into completely point cloud, so as to follow-up unity and coherence in writing mapping addition and cavity reparation etc.
The carrying out of operation.
Elements of contacting net partial dot cloud data visualization to be reconstructed is obtained after data preprocessing as shown in Figure 4.
C, each visual angle three dimensional point cloud registration
Key point extraction and description are carried out using algorithms of the SIFT of the present invention in combination with LBP, and determines correspondence pass
System, then Jing point cloud rough registrations and ICP essence registration methods carry out point cloud registering, the complete elements of contacting net to be reconstructed three-dimensional of acquisition
Cloud data.Key point extraction effect is as shown in figure 5, contrast is as shown in fig. 6, obtained complete point cloud data can before and after point cloud registering
It is as shown in Figure 7 depending on changing.
A, point cloud rough registration adopt PCA (PCA：Principal Components Analysis)
Initial coordinate conversion between point cloud is obtained using PCA methods, so as to realize the rough registration between a cloud.Used by the method
The covariance matrix for arriving is as follows：
In formula
Target point set P and source point collection Q are substituted into into respectively covariance matrix and using SVD decomposition methods, it is final to obtain initial rotation
Torque battle array R and translation vector t：
R=UPUQ -1
U in formulaP, UQIt is respectively the SVD split-matrixes of point set P and Q covariance matrix；It is respectively point set P and Q
Central point.
B, ICP essence registration
To realize high accuracy point cloud registering, using ICP point cloud registration algorithms most widely used at present.From the point of Jing rough registrations
Correspondence point set P and Q are determined according to certain criterion in cloud, then optimum coordinate transform are iterated to calculate according to method of least square,
Make error function minimum.Error function is defined as：
ICP essence registration Algorithm flow processs are as follows：
1) target point set P and reference source point set Q are obtained (two point set numbers are equal)；
2) match point purification processes, obtain in P N number of feature point group into feature point set S0；
3) (k=0) is initialized, initial transformation matrix T obtained by rough registration0Enter line translation S to feature point set1=T
(S0)；
4) feature point set S is found in reference source point set QkClosest approach Sk', become by two corresponding point set coordinates computeds
Change matrix Tk；
5) coordinate transform is carried out to feature point set using the transformation matrix of coordinates for obtaining：Sk+1=Tk(Sk)；
6) whether error in judgement is less than given threshold, if dk-dk+1＜ τ, then iteration terminate, otherwise, go to 4)；
7) determine that final coordinate is converted, realize point cloud essence registration：P'=T (P).
C, Algorithm Analysis
Algorithm of the present invention is used for the registration of three-dimensional point cloud, mainly retouches in key point characteristic vector compared with SIFT algorithms
The structure aspect stated changes.SIFT algorithms need to build the vector of one 128 dimension with regard to key point description, and this is significantly impacted
The speed of the algorithm, and it is computationally intensive.And the method for the invention is carrying out meter involved when key point characteristic vector builds
It is the exponent arithmetic of some relatively simple arithmetic operators and vector dimension size to calculate, therefore is calculated compared to SIFT with Quasi velosity
Method is fast.For 20, the method is designated as LBP-20 to the description vectors dimension that the LBP methods that this example is adopted are used.This paper algorithms
Realize that the comparison of two kinds of algorithm speeds is as shown in Figure 8 in C++ environment in binding site cloud storehouse (PCL).
Analysis Fig. 8 data understand that the time used by SIFT algorithms is context of methods use time in key point description
15.264 times, and the former is 2.102 times of the latter to match the time used.It is demonstrated experimentally that set forth herein algorithm meet expection,
The speed of registration can be improved, so as to accelerate process of reconstruction.
D, curve reestablishing
After acquiring elements of contacting net complete point cloud data to be reconstructed, curve reestablishing need to be carried out, to obtain three-dimensional
Model, the present invention completes curve reestablishing using Poisson curved planar reformation, rebuilds effect as shown in Figure 9.
Embodiment
Below by the method for the invention be used for contact net in rod insulator, section insulator, disc insulator three
Dimension is rebuild.Process of reconstruction is consistent with specific implementation process of the present invention, shown in income effect accompanying drawing.Rod insulator material object and model
Compares figure is as shown in Figure 10, and with threedimensional model compares figure as shown in figure 11, disc insulator is in kind and weighs for section insulator material object
Established model compares figure is as shown in figure 12.
Understand that the present invention is obtained in that ideal elements of contacting net Three-dimension Reconstruction Model from algorithm examples.
Claims (1)
1. a kind of elements of contacting net three-dimensional rebuilding method of the point cloud registering based on SIFT and LBP, is obtained by Kinect device
Elements of contacting net three dimensional point cloud to be reconstructed is taken, comprising following means：
(1), elements of contacting net three dimensional point cloud is obtained and pretreatment
Oni format video numbers are obtained using Kinect for Windows equipment and with reference to the Niviewer.exe in OpenNI
According to, then with point a cloud storehouse PCL convert video data to pcd form cloud data files, so as to obtain contact net to be reconstructed
The initial three-dimensional data of parts place environment；Initial three dimensional point cloud to getting carry out denoising, simplification, segmentation cluster,
Fusion pretreatment operation, obtains elements of contacting net three dimensional point cloud to be reconstructed；
(2), scale invariant feature is used to three dimensional point cloud under each visual angle of elements of contacting net to be reconstructed acquired in ()
Conversion SIFT (Scale Invariant Feature Transform) algorithm, extracts SIFT key points；Then, using uniform
Image local binary pattern (the LBP of pattern：Local Binary Patterns) feature description is carried out to key point, obtain each
Key point feature description vector；Then, measure distance between vector as similarity determination between key point, and difference is determined with this
The corresponding relation between cloud is put under visual angle；Finally, a cloud rough registration and closest approach iteration ICP (Iterative Closest are carried out
Point) essence registration, obtains elements of contacting net Complete three-dimensional cloud data to be reconstructed；
(3), curve reestablishing is carried out to (two) data using Poisson curved planar reformation, hole repair, texture is carried out to obtained model
Addition, finally obtains the threedimensional model of elements of contacting net to be reconstructed, completes process of reconstruction；
The concrete steps that (two) and (three) implement are included：
(1) SIFT key points are extracted
A, metric space feature point detection, i.e., detect Local Extremum in difference of Gaussian pyramid, waits in this, as key point
Object is selected, metric space used and difference of Gaussian function are as follows,
Metric space：
Difference of Gaussian function：D (x, y, σ)=L (x, y, k σ)-L (x, y, σ)
G (x, y, σ) is gaussian kernel,I (x, y) is image intensity；σ yardsticks；K is constant；
B, key point are accurately positioned, yardstick determines and the rejecting of unstable candidate key point；By the extreme value of digital simulation curved surface
To determine exact position and the yardstick of key point, while the low characteristic point of contrast and unstable skirt response point are rejected, with
Improve the stability and noise immunity of matching；
The determination of C, key point principal direction；The gradient-norm of each pixel and direction are respectively in metric space：
θ (x, y)=tan-1((L(x,y+1)-L(x,y-1))/(L(x+1,y)-L(x-1,y)))
Gradient orientation histogram is created, selects histogrammic main peak value to be key point principal direction；
(2) the invariable rotary uniform pattern LBP feature descriptions of key point peripheral region
A, in SIFT key points piIn the k nearest neighbor region of (x, y, z, σ, α, beta, gamma), respectively with each point pjCentered on, try to achieve with
Invariable rotary uniform pattern LBP features centered on itIt is designated as lbpj(j=1,2 ..., K)；
gi、gcIt is respectively the gray value of the gray value of sampled point and intermediary image vegetarian refreshments in neighborhood；P is sampling number；R is sampling half
Footpath；
B, addition weighted value, ωj=exp (- (d2/(2σ0 2)))/(2πσ0 2)；
D is point pjWith key point piBetween distance；σ0For the constant selected；
C, characteristic vector build, Ti=[ω1·lbp1 ω2·lbp2 … ωK·lbpK]；
D, normalized eliminate illumination effect, i.e.,
(3) SIFT keys Point matching, determines corresponding relation；
Decision metric is the distance between vector, is expressed as follows：
TA, TBIt is respectively the LBP feature descriptions vector of key point A and B；ai、biBe respectively A and B LBP feature descriptions vector it is each
Dimension element；
Matching strategy is：Key point A in a cloud 1 is taken, two passes nearest with its feature description vector distance are found out in a cloud 2
Key point B and C, if minimum distance is less than certain threshold value t with secondary in-plant ratio, then it is assumed that the pass closest with key point A
Key point B matches with it, i.e.,
(4) point cloud registering
After 2 cloud corresponding relations determine, registration is carried out to a cloud, rough registration and essence two processes of registration can be divided into；Rough registration
Using PCA PCA (Principal Components Analysis), essence registration is using ICP essence registration methods；Jing mono-
Serial point cloud registering obtains complete elements of contacting net three dimensional point cloud to be reconstructed；
(5) using Poisson curved planar reformation, curve reestablishing is carried out to obtained complete point cloud data, obtains zero, contact net to be reconstructed
Part threedimensional model；
The registration of three-dimensional reconstruction process point cloud is carried out according to this point cloud registration method, accelerates point cloud registering speed, so as to add
Fast process of reconstruction, obtains elements of contacting net threedimensional model to be reconstructed；
More than the definition of other each symbols and variable be：(x, y) is space pixel coordinate；Represent convolution algorithm；σ is yardstick；σ
Size determines the smoothness of image, the general picture feature of large scale correspondence image, the minutia of little yardstick correspondence image；Big
σ values correspondence coarse scale is low resolution, conversely, correspondence fine dimension is high-resolution；
σ (s)=2o-1σ0·2s/S, o be pyramid group number, o=[log2(min (m, n))] -3, m, n be two dimensional image height and width, s
It is every group of middle level coordinate, σ0For initial gauges, S is every group of number of plies, and S is generally 3~5；K is two neighboring metric space multiple
Constant, k=21/S；α, β, γ are that each coordinate surface of 3-D view key point projects principal direction.
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